Finite Group Databasebeta

← #25199691

Subgroups — #25199691

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142977C211yesmaximal, characteristic, complemented
2#19136097C211yesmaximal, characteristic, complemented
3#19135987C211yesmaximal, characteristic, complemented
4#19135983C211yesmaximal, characteristic
5#19135912C211yesmaximal, characteristic
6#19135448C211yesmaximal, characteristic
7#19135325C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic
9#19135270C211yesmaximal, characteristic, complemented
10#19135236C211yesmaximal, characteristic, complemented
11#19135173C211yesmaximal, characteristic, complemented
12#19134929C211yesmaximal, characteristic
13#19134842C211yesmaximal, characteristic
14C4×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#2293C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582783—21no—
37#14582783—21no—
38#14582783—21no—
39#14582767—21no—
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×D4×C43C2211yescharacteristic
49C2×#117×C43—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C43×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73#13063258—22no—
74#13063258—41no—
75#13063256—22no—
76C4⋊(C43⋊C8)—22no—
77C4⋊(C43⋊C8)—22no—
78#13063248—22no—
79#13063248—22no—
80#13063248—41no—
81#13063246—22no—
82#13063246—22no—
83#13063246—41no—
84C4×C43⋊C8—41no—
85C4×C43⋊C8—41no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×D4×C43C2311yescharacteristic
96C23×C4×C43—21no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99#117×C43—44no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43D411yescharacteristic
112C2×C42×C43D411yescharacteristic
113C2×C42×C43D411yescharacteristic
114C2×C42×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121C24×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43#4112yes—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43#4112yes—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—42no—
162C22⋊C4×C43—42no—
163C22⋊C4×C43—42no—
164C42×C43—22no—
165C42×C43—22no—
166C42×C43—22no—
167C42×C43—22no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—42no—
175#10621883—44no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8#4112yes—
196C2×C43⋊C8#4112yes—
197C23×C43—22no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C22×D411yescharacteristic
205D4×C43—22no—
206D4×C43—22no—
207D4×C43—41no—
208D4×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—48no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43#13512yes—
234C2×C4×C43#13512yes—
235C2×C4×C43AGL(1,ℤ/8)12yes—
236C2×C4×C43#13712yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258Dic86—41no—
259C43⋊C8—22no—
260C43⋊C8—22no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#29433—431nomaximal, Sylow
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#52511yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#53711yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#55111yescharacteristic
288C4×C43#55211yescharacteristic
289C4×C43#55311yescharacteristic
290C4×C43#55611yescharacteristic
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#2863—431no—
296#2293D4311yescharacteristic
297#2088—431no—
298#2068—431no—
299#2067—431no—
300#2055—431no—
301#1968—431no—
302#1942—431no—
303#1934—431no—
304#1933—431no—
305#1928—431no—
306#1919—431no—
307#1877—431no—
308#1862—431no—
309C4×C4⋊C8—431no—
310C2×C43—82no—
311C2×C43#260111yescharacteristic
312C2×C43#310511yescharacteristic
313C2×C43#310711yescharacteristic
314C2×C43#316811yescharacteristic
315C2×C43#318211yescharacteristic
316C2×C43#324711yescharacteristic
317C2×C43#324811yescharacteristic
318C22×SD16—431no—
319C2×C4×D4C2×D4311yescharacteristic
320C2×#117—21no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#106—431no—
324C2×C4⋊C8—431no—
325C2×C4⋊C8—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334#391—431no—
335#391—431no—
336#391—431no—
337#390C2×D4311yescharacteristic
338#390C2×D4311yescharacteristic
339#389—431no—
340#389—431no—
341#389—431no—
342#389C2×D4311yescharacteristic
343#389C2×D4311yescharacteristic
344#388—21no—
345#388—21no—
346#387—861no—
347#387—861no—
348#387—861no—
349#383—861no—
350C4×C4⋊C4C2×D4311yescharacteristic
351C4×C22⋊C4—21no—
352C43C2×D4311yescharacteristic
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#336—431no—
360#336—431no—
361C43#2943311yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—21no—
365C2×SD16—862no—
366C2×SD16—862no—
367C2×SD16—1721no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8—431no—
371C22×C8—431no—
372C4×D4—22no—
373C4×D4—22no—
374#117—44no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42C22⋊D4311yescharacteristic
393C2×C42C22⋊D4311yescharacteristic
394C2×C42C22⋊D4311yescharacteristic
395C2×C42C22⋊D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398C2×C42C22×D4311yescharacteristic
399#107—862no—
400#107—1721no—
401#106—862no—
402C4⋊C8—862no—
403C4⋊C8—862no—
404#103—862no—
405#103—862no—
406#103—1721no—
407#102—862no—
408#102—862no—
409#102—1721no—
410C4×C8—1721no—
411C4×C8—1721no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—21no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4#1062189812yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454SD16—1724no—
455C2×C8—432no—
456C2×C8—432no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4#1062189812yes—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D4311yescharacteristic
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—48no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4#1306334512yes—
553C2×C4#1306334512yes—
554C2×C4#1306335112yes—
555C2×C4#1306335512yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4C2×#1062189811yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—862no—
563C8—862no—
564C8—1721no—
565C8—1721no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1458341011yescharacteristic
574C22#1458344511yescharacteristic
575C22#1458347711yescharacteristic
576C22C2×#1306334511yescharacteristic
577C22C2×#1306334511yescharacteristic
578C22C2×#1306335111yescharacteristic
579C22C2×#1306335511yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—3441no—
593C4#1458357311yescharacteristic
594C4#1458358211yescharacteristic
595C4#1458359311yescharacteristic
596C4#1458361711yescharacteristic
597C2—82no—
598C2#1914019211yescharacteristic
599C2#1914464211yescharacteristic
600C2#1914466611yescharacteristic
601C2#1914515911yescharacteristic
602C2#1914530911yescharacteristic
603C2#1914591511yescharacteristic
604C2#1914593211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2293C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2293D43
hypocenterC43#29433
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19142977C2semidirect
2. #19136097C2semidirect
3. #19135987C2semidirect
7. #19135325C2semidirect
9. #19135270C2semidirect
10. #19135236C2semidirect
11. #19135173C2semidirect
14. C4×C4⋊(C43⋊C8)C2semidirect
361. C43#29433semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191429772
#191360972
#191359872
#191359832
#191359122
#191354482
#191353252
#191352812
#191352702
#191352362
#191351732
#191349292
#191348422
C4×C4⋊(C43⋊C8)2
C43×#22932
#2943343